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Congruence semimodular varieties I: Locally finite varieties

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References

  1. Agliano, P.,Algebras whose congruence lattices are semimodular, Ph.D. Thesis, University of Hawaii, 1988.

  2. Agliano, P. andKearnes, K.,Congruence semimodular varieties II: Regular varieties, Algebra Universalis32 (1994), 270–296.

    Google Scholar 

  3. Crawley, P. andDilworth, R. P.,Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, NJ, 1973.

    Google Scholar 

  4. Day, A.,A characterization of modularity for congruence lattices of algebras, Can. Math. Bull.12 (1969), 167–173.

    Google Scholar 

  5. Freese, R. andMcKenzie, R.,Commutator Theory for Congruence Modular Varieties, LMS Lecture Note Series 125, Cambridge University Press, 1987.

  6. Hall, T. E.,On the lattice congruences on a semilattice, J. Austral. Math. Soc.12 (1971), 456–460.

    Google Scholar 

  7. Hobby, D. andMcKenzie, R.,The Structure of Finite Algebras, Contemporary Mathematics, American Mathematical Society, Providence RI, 1988.

    Google Scholar 

  8. Jones, P.,Congruence semimodular varieties of semigroups, Semigroups, theory and applications (Oberwolfach 1986), Springer Lecture Notes in Math. No. 1320 (1988).

  9. Jónsson, B.,Algebras whose congruence lattices are distributive, Math. Scand.21 (1967), 110–121.

    Google Scholar 

  10. Kearnes, K.,Atomicity and Nilpotence, Can. J. Math.42 (1990), 365–382.

    Google Scholar 

  11. Kearnes, K.,Congruence lower semimodularity and 2-finiteness imply congruence modularity, Algebra Universalis28 (1991), 1–11.

    Google Scholar 

  12. Kearnes, K.,Relatively congruence distributive subquasivarieties of a congruence modular variety, Bull. Austral. Math. Soc.41 (1990), 87–96.

    Google Scholar 

  13. Kearnes, K.,Type preservation in locally finite varieties with the CEP, Can. J. Math.43 (1991), 748–769.

    Google Scholar 

  14. Kearnes, K. andMcKenzie, R.,Commutator theory for relatively modular quasivarieties, Trans. Amer. Math. Soc.331 (1992), 465–502.

    Google Scholar 

  15. Kiss, E.,Each Hamiltonian variety has the congruence extension property, Algebra Universalis12 (1981), 395–398.

    Google Scholar 

  16. Kiss, E. andPröhle, P.,Problems and results in tame congruence theory (A survey of the '88 Budapest workshop), Algebra Universalis29 (1992), 151–171.

    Google Scholar 

  17. Kiss, E. andValeriote, M.,Abelian algebras and the Hamiltonian property, J. Pure and Applied Algebra87 (1993), 37–49.

    Google Scholar 

  18. Mal'cev, A. I.,On the general theory of algebraic systems, Mat. Sbornik77 (1954), 3–20.

    Google Scholar 

  19. McKenzie, R., McNulty, G. andTaylor, W.,Algebras, Lattices, Varieties, Vol I, Wadsworth and Brooks Cole, Monterey, California, 1987.

    Google Scholar 

  20. Ore, O.,Theory of equivalence relations, Duke Math. J.9 (1942), 573–627.

    Google Scholar 

  21. Taylor, W.,Characterizing Mal'cev conditions, Algebra Universalis3 (1973), 351–397.

    Google Scholar 

  22. Taylor, W.,The fine spectrum of a variety, Algebra Universalis5 (1975), 263–303.

    Google Scholar 

  23. Valeriote, M.,On Decidable Locally Finite Varieties, Ph.D. Dissertation, U.C. Berkeley, 1986.

    Google Scholar 

  24. Kearnes, K.,A hamiltonian property for nilpotent algebras, preprint, 1994.

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Dedicated to Bjarni Jónsson on the occasion of his 70th birthday

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Agliano, P., Kearnes, K.A. Congruence semimodular varieties I: Locally finite varieties. Algebra Universalis 32, 224–269 (1994). https://doi.org/10.1007/BF01191540

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